Proc. of Workshop on Mechanics of Quasi-Brittle Materials and Structures,
Prague, 27-28 March 1998,
ed. G. Pijaudier-Cabot, Z. Bittnar, and B. Gérard, Hermès Science Publications, Paris, 57-77.


Milan Jirásek
Swiss Federal Institute of Technology
LSC -DGC, EPFL, 1015 Lausanne, Switzerland


This paper discusses several aspects of constitutive modeling based on the microplane concept. The common idea is a systematic and consistent application of the principle of virtual work. The first part focuses on microplane damage models derived from the principle of energy equivalence. The second part addresses theoretical problems related to the extension of microplane models into the large-strain range. Finally, certain considerations regarding the symmetry of Cauchy stress tensor lead to the idea of a micropolar (Cosserat-type) microplane model.


The first part of the paper has been concerned with microplane damage models based on the principle of energy equivalence. The theoretical basis originally proposed by Carol and Bazant (1997) has been reformulated and generalized. It has been demonstrated that a consistent variational approach leads to the sum-type symmetrization of the damage effect tensor. The abstract general framework has been specialized into a particular formulation intended for anisotropic damage modeling of concrete fracture. The compliance version seems to give better numerical results than the stiffness version.

In the second part, several new ideas related to the large-strain extension of microplane models have been advanced. Attention has been focused on the derivation of the stress evaluation formula from the principle of virtual work. As an alternative to the procedure proposed by Bazant et al. (1998), an approach leading directly to the Cauchy stress tensor has been advocated. Its salient feature is that it is intrinsically objective. No polar decomposition of the deformation gradient is required, and no objective stress rate has to be defined. Objectivity (frame invariance) is achieved by relating all quantities on the microplane level to a local coordinate system that travels with the microplane. A natural generalization of this approach leads to a micropolar (Cosserat-type) version of the microplane model.

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EPFL / 14 January 1999 /